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Hierarchical Linear Models: Applications and Data Analysis Methods (Advanced Quantitative Techniques in the Social Sciences)

Stephen W. Raudenbush, Anthony S. Bryk

Hierarchical Linear Models: Applications and Data Analysis Methods (Advanced Quantitative Techniques in the Social Sciences) Stephen W. Raudenbush, Anthony S. Bryk Amazon Price: $95.20
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Customer Reviews:
Total reviews: 3 Average rating: 3.5 of 5

Editorial Review:

"This is a first-class book dealing with one of the most important areas of current research in applied statistics…the methods described are widely applicable…the standard of exposition is extremely high."
--Short Book Reviews from the International Statistical Institute

"The new chapters (10-14) improve an already excellent resource for research and instruction. Their content expands the coverage of the book to include models for discrete level-1 outcomes, non-nested level-2 units, incomplete data, and measurement error---all vital topics in contemporary social statistics. In the tradition of the first edition, they are clearly written and make good use of interesting substantive examples to illustrate the methods. Advanced graduate students and social researchers will find the expanded edition immediately useful and pertinent to their research."
--TED GERBER, Sociology, University of Arizona

"Chapter 11 was also exciting reading and shows the versatility of the mixed model with the EM algorithm. There was a new revelation on practically every page. I found the exposition to be extremely clear. It was like being led from one treasure room to another, and all of the gems are inherently useful. These are problems that researchers face everyday, and this chapter gives us an excellent alternative to how we have traditionally handled these problems."
--PAUL SWANK, Houston School of Nursing, University of Texas, Houston

Popular in the First Edition for its rich, illustrative examples and lucid explanations of the theory and use of hierarchical linear models (HLM), the book has been reorganized into four parts with four completely new chapters. The first two parts, Part I on "The Logic of Hierarchical Linear Modeling" and Part II on "Basic Applications" closely parallel the first nine chapters of the previous edition with significant expansions and technical clarifications, such as:

* An intuitive introductory summary of the basic procedures for estimation and inference used with HLM models that only requires a minimal level of mathematical sophistication in Chapter 3
* New section on multivariate growth models in Chapter 6
* A discussion of research synthesis or meta-analysis applications in Chapter 7
* Data analytic advice on centering of level-1 predictors and new material on plausible value intervals and robust standard estimators

While the first edition confined its attention to continuously distributed outcomes at level 1, this second edition now includes coverage of an array of outcomes types in Part III:

* New Chapter 10 considers applications of hierarchical models in the case of binary outcomes, counted data, ordered categories, and multinomial outcomes using detailed examples to illustrate each case
* New Chapter 11 on latent variable models, including estimating regressions from missing data, estimating regressions when predictors are measured with error, and embedding item response models within the framework of the HLM model
* New introduction to the logic of Bayesian inference with applications to hierarchical data (Chapter 13)

The authors conclude in Part IV with the statistical theory and computations used throughout the book, including univariate models with normal level-1 errors, multivariate linear models, and hierarchical generalized linear models.

A First Course in Optimization Theory

Rangarajan K. Sundaram

A First Course in Optimization Theory Rangarajan K. Sundaram Amazon Price: $35.09
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Customer Reviews:
Total reviews: 10 Average rating: 4.0 of 5

Couldn't ask for much more. 5 out of 5 stars.
6 of 7 people found this review helpful.

An excellent introduction at this level which is both lucid and rigorous with just enough examples to motivate applications while not leaving the reader swimming in redundancy. The previous review gives details, but I will add that the proofs are concise and clear. The only thing I would add to this book is more and harder problems, but that is easily remedied. If you want a theoretical introduction, buy this book right now -- its one of the best textbooks I have ever seen.

Editorial Review:

This book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

Numerical Optimization (Springer Series in Operations Research and Financial Engineering)

Jorge Nocedal, Stephen Wright

Numerical Optimization (Springer Series in Operations Research and Financial Engineering) Jorge Nocedal, Stephen Wright Amazon Price: $79.95
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Total reviews: 13 Average rating: 4.5 of 5

Editorial Review:

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

There is a selected solutions manual for instructors for the new edition.

Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6) (Athena Scientific Series in Optimization and Neural Computation, 6)

Dimitris Bertsimas, John N. Tsitsiklis

Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6) (Athena Scientific Series in Optimization and Neural Computation, 6) Dimitris Bertsimas, John N. Tsitsiklis Amazon Price: $89.00
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Customer Reviews:
Total reviews: 10 Average rating: 5.0 of 5

Nice intuition and good coverage 5 out of 5 stars.
4 of 4 people found this review helpful.

The best part of this book is the first half, where the foundations of linear programming are presented in a clear yet relatively rigorous fashion, accompanied by numerous intuitive geometrical explanations of the abstract general concepts. This approach, supplementing mathematics with graphical insights, works extremely well for this topic.

The quality goes down somewhat, perhaps neccessarily, in the latter half of the book as topics are presented less carefully, and in a somewhat rushed manner in order to cover all of the material the authors decided to include. Given that the fundamentals are covered so well, perhaps this is a fair trade.

The only real negative I can think of is that it's a small crime for professors to create their own publishing companies (Athena only publishes works by a small group of MIT professors) and then still charge outrageous amounts for the books. This would be completely unacceptable were it not for the fact that, unlike most self-published work, this book's production quality is on par with that of the large publishers.

Editorial Review:

This book provides a unified, insightful, and modern treatment of linear optimization, that is, linear programming, network flow problems, and discrete optimization. It includes classical topics as well as the state of the art, in both theory and practice.

Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models (Texts in Statistical Science)

Julian J. Faraway

Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models (Texts in Statistical Science) Julian J. Faraway Amazon Price: $71.96
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Total reviews: 1 Average rating: 4.0 of 5

Editorial Review:

Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. A supporting Web site at www.stat.lsa.umich.edu/~faraway/ELM holds all of the data described in the book. Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught.

How to Solve It: Modern Heuristics

Zbigniew Michalewicz, David B. Fogel

How to Solve It: Modern Heuristics Zbigniew Michalewicz, David B. Fogel Amazon Price: $47.96
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Customer Reviews:
Total reviews: 18 Average rating: 4.5 of 5

It's not the technique, it's the logic behind it 4 out of 5 stars.
6 of 7 people found this review helpful.

Most evolutionary computation or math books deal with the techniques of solving problems. This book teachs you how to think of a solution for the problem you face, and not what problems are appropriate for the technique in hand.

The logic is that when you do a craft work, you do pick the appropriate tool from your tools box, but you don't grasp a tool and then find a job to go with it, which is the case when you can only handle this tool.

Editorial Review:

This book is the only source that provides comprehensive, current, and correct information on problem solving using modern heuristics. It covers classic methods of optimization, including dynamic programming, the simplex method, and gradient techniques, as well as recent innovations such as simulated annealing, tabu search, and evolutionary computation. Integrated into the discourse is a series of problems and puzzles to challenge the reader. The book is written in a lively, engaging style and is intended for students and practitioners alike. Anyone who reads and understands the material in the book will be armed with the most powerful problem solving tools currently known.

This second edition contains two new chapters, one on coevolutionary systems and one on multicriterial decision-making. Also some new puzzles are added and various subchapters are revised.

Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley Series in Probability and Statistics)

Warren B. Powell

Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley Series in Probability and Statistics) Warren B. Powell Amazon Price: $93.56
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Total reviews: 3 Average rating: 5.0 of 5

Editorial Review:

A complete and accessible introduction to the real-world applications of approximate dynamic programming

With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines-Markov design processes, mathematical programming, simulation, and statistics-to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems.

Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues.

With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming:
*

Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects
*

Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics
*

Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms
*

Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book

Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.

Dynamic Programming

Richard Bellman

Dynamic Programming Richard Bellman Amazon Price: $13.57
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Total reviews: 1 Average rating: 4.0 of 5

A classic book on Dynamic Programming 4 out of 5 stars.
1 of 2 people found this review helpful.

It's a classic book on Dynamic Programming by its own creator, Richard Bellman. The mathematical models are always supported by good examples. However, the mathematical formalism is hold and quite different from what someone can find in the more modern references.

Editorial Review:

An introduction to the mathematical theory of multistage decision processes, this text takes a "functional equation" approach to the discovery of optimum policies. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, multistage games, and more. 1957 edition. Includes 37 figures.

Generalized Linear Models, Second Edition (Monographs on Statistics and Applied Probability)

P. McCullagh, John A. Nelder

Generalized Linear Models, Second Edition (Monographs on Statistics and Applied Probability) P. McCullagh, John A. Nelder Amazon Price: $79.96
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Total reviews: 5 Average rating: 5.0 of 5

Editorial Review:

The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications. The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables. The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions. Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.

Convex Analysis (Princeton Landmarks in Mathematics and Physics)

Ralph Tyrell Rockafellar

Convex Analysis (Princeton Landmarks in Mathematics and Physics) Ralph Tyrell Rockafellar Amazon Price: $41.97
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Total reviews: 4 Average rating: 4.0 of 5

Editorial Review:

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.

This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.


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